Is it possible to don't display the previous random item from a list?

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C#

Like the question says, is it possible to not display the previous random item from a list? basically I have a List:

List<Animal> animals = new List();

That have the following properties

public string Name
{
    get { return _name; }
    set { _name = value; }
}

public string Specie
{
    get { return _specie; }
    set { _specie = value; }
}

What I have tried:

This object name or specie is then being randomly generated to text boxes:

private string RandomAnimal(Random r)
{
    if (random.Next(2) == 0)
    {
        txtSpecie.Text = randomAnimal.Specie;
        return randomAnimal.Specie;
    }
    else
    {
        txtName.Text = randomAnimal.Name;
        return randomAnimal.Name;
    }
}

Lets say that random animal Name has been shown on the textbox. Is it possible to write a method perhaps that will insure that the same name that was previously displayed in textbox will not be displayed anymore?

Thanks in advance